A digital-to-analog converter (DAC) converts a digital input code to an analog output signal. The output of a DAC may deviate from the ideal output due to variations in the manufacturing process and due to various sources of inaccuracy in the digital-to-analog conversion process. The transfer function of a DAC is a plot of the signal generated at the DAC output as function of the input code. Such a plot is not continuous but is a plot of 2N steps, where N is the resolution of the DAC in bits. For an ideal DAC, a single straight line can be drawn through the points at each code-transition boundary, beginning at the origin of the plot.
FIG. 1 shows a plot 10 an example of an ideal transfer function 12 for a 3-bit DAC with reference points at code transition boundaries. The DAC in this example produces a total of eight steps that each represents a value of a digital input code. The output signal reaches a minimum at code zero (000) and a maximum at code (111). Thus, the transition to the maximum output does not occur at voltage reference, Vref. The transition occurs at one code width, which is equal to a least significant bit (LSB). An LSB is Vref/2N.
Limitations in the materials used in fabrication and inaccuracies inherent in the conversion process itself cause the actual transfer function of a DAC to deviate from the ideal transfer function.
The deviation of a DAC's transfer function from a straight line is referred to as non-linearity. FIG. 2 illustrates a plot 20 of non-linear deviation between the ideal 12 transfer function and the actual transfer function 22 the exemplary 3-bit DAC. The differences between the ideal voltage levels at which code transitions occur and the actual voltage are referred to as non-linear errors. Non-linear errors may be expressed in LSBs (e.g., 1.3 LSB).
Nonlinearity affects performance, which is often characterized using parameters obtained via frequency-domain analysis and is typically measured by performing a fast Fourier transform (FFT) on the analog output of the DAC. FIG. 3 shows a plot 30 of the DAC output in the frequency domain. The fundamental frequency is equal to the frequency of the digital input (i.e., the signal measured with the DAC). All other frequency components are unwanted signals that result from harmonic distortion, thermal noise, 1/f noise, and quantization noise. Some sources of noise may not originate from the DAC itself. For example, distortion and thermal noise originate from the external circuit at the input to the DAC.
Nonlinearity in the data converter results in harmonic distortion when analyzed in the frequency domain. Such distortion is observed as “spurs” in the FFT at harmonics of the measured signal as illustrated in FIG. 3. Nonlinearity also produces spurs within the Nyquist frequency of the DAC at frequencies that are not harmonics of the fundamental frequency. The ratio between the magnitude of the measured signal and its highest spur peak is referred to as “spurious-free dynamic range” (SFDR), and is often expressed in decibels (dB). The highest spur could be a harmonic of the measured signal or non-harmonic component, depending on the application. SFDR depends on the fundamental frequency of the input signal. As the fundamental frequency increases, the SFDR tends to decrease.